10MB is pushing it but you'll probably be OK.
Protobuf has a hard limit of 2GB, because many implementations use 32-bit signed arithmetic. For security reasons, many implementations (especially the Google-provided ones) impose a size limit of 64MB by default, although you can increase this limit manually if you need to.
The implementation will not "slow down" with large messages per se, but the problem is that you must always parse an entire message at once before you can start using any of the content. This means the entire message must fit into RAM (keeping in mind that after parsing the in-memory message objects are much larger than the original serialized message), and even if you only care about one field you have to wait for the whole thing to parse.
Generally I recommend trying to limit yourself to 1MB as a rule of thumb. Beyond that, think about splitting the message up into multiple chunks that can be parsed independently. However, every application -- for some, 10MB is no big deal, for others 1MB is already way too large. You'll have to profile your own app to find out.
I've actually seen cases where people were happy sending messages larger than 1GB, so... it "works".
On a side note, Cap'n Proto has a very similar design to Protobuf but can support messages up to 2^64 bytes (2^32 segments of 4GB each), and it actually does allow you to read one field from the message without parsing the whole message (if it's in a file on disk, use mmap() to avoid reading the whole thing in).
(Disclosure: I'm the author of Cap'n Proto as well as most of Google's open source Protobuf code.)
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